What are the solutions to the equation (x^2+2)/2 =(7x-5)/3 ?

The solutions to the equation (x^2+2)/2 =(7x-5)/3 are x= 8/3 ,x=2

Find the zeros of (x^2+2)/2 =(7x-5)/3

The zeros of (x^2+2)/2 =(7x-5)/3 are x= 8/3 ,x=2

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\frac{x ^{2} + 2}{2} = \frac{7 x - 5}{3}

x = \frac{8}{3}, x = 2

Decimal Notation

x = 2.66666 \dots, x = 2

Solution steps

\frac{x ^{2} + 2}{2} = \frac{7 x - 5}{3}

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

\frac{x ^{2} + 2}{2} \cdot 6 = \frac{7 x - 5}{3} \cdot 6

Simplify

3 (x^{2} + 2) = 2 (7 x - 5)

Expand

3 (x^{2} + 2) : 3 x^{2} + 6

Expand

2 (7 x - 5) : 14 x - 10

3 x^{2} + 6 = 14 x - 10

Move

10

to the left side

3 x^{2} + 16 = 14 x

Move

14 x

to the left side

3 x^{2} + 16 - 14 x = 0

Write in the standard form

a x^{2} + b x + c = 0

3 x^{2} - 14 x + 16 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 3 \cdot 16}{2 \cdot 3}

(- 14)^{2} - 4 \cdot 3 \cdot 16 = 2

x_{1, 2} = \frac{- ( - 14 ) \pm 2}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 14 ) + 2}{2 \cdot 3}, x_{2} = \frac{- ( - 14 ) - 2}{2 \cdot 3}

x = \frac{- ( - 14 ) + 2}{2 \cdot 3} : \frac{8}{3}

x = \frac{- ( - 14 ) - 2}{2 \cdot 3} : 2

The solutions to the quadratic equation are:

x = \frac{8}{3}, x = 2

a, \frac{1 ( a + 7 ) ( ab )}{2} = c (c + d) d

x, x^{2} + y^{2} + z^{2} = 13

x, x^{2} + y^{2} + z^{2} = 10

(x) = 4 x^{2} - 9 x + 16

x^{2} - 3 x + 2 = 0, (1, - 1, 2, - 2)

What are the solutions to the equation (x^2+2)/2 =(7x-5)/3 ?
The solutions to the equation (x^2+2)/2 =(7x-5)/3 are x= 8/3 ,x=2
Find the zeros of (x^2+2)/2 =(7x-5)/3
The zeros of (x^2+2)/2 =(7x-5)/3 are x= 8/3 ,x=2